1. Field of the Invention
The present invention relates to a hologram scanner and a method of recording and reproducing a hologram in the hologram scanner, which is used in an image forming apparatus such as a laser beam printer, and an image reading apparatus.
2. Description of the Related Art
In various kinds of scanning devices used in an image forming apparatus and an image reading apparatus, there is a hologram scanner, which utilizes a hologram as means for deflecting a light beam for scanning.
The hologram scanner has a hologram disk on which a plurality of holograms are arranged along its circumferential direction. When the hologram disk rotates, the reproducing light beam is deflected by the diffraction effect of the hologram. The hologram scanner scans an image surface by the deflected diffraction light beam in a main scanning direction.
Such a hologram is recorded and manufactured by a mutual interference of two light fluxes, i.e. an object light of laser beam and a reference light of laser beam. If a non-aberrational spherical wave or a non-aberrational plane wave are utilized as these two light fluxes, interference fringes are obtained which are represented by quadratic curves, such as circular curves, elliptic curves, parabolic curves, and hyperbolic curves. Accordingly, the hologram is recorded so as to have a desired diffraction power, a desired diffraction direction, a desired focusing power etc., by adjusting the pitch and the shape of the interference fringes.
The hologram thus recorded has a function of focusing the reproducing light beam so as to form a light spot on the image surface as well as the function of deflecting the reproducing light beam.
Methods of recording and reproducing such a hologram can be divided into some cases according to the kinds of the object light, the reference light and the reproducing light, as explained below.
Namely, in a first case, a hologram recorded by the mutual interference of a spherical divergent wave as the object light and a plane wave as the reference light, is reproduced by a collimated reproducing light beam. In this first case, the distance from the hologram to the center of the reproducing light source is infinity, and thus the reproducing light beam diffracted by the hologram is converged at the focal point of the hologram.
In a second case, a hologram recorded by the mutual interference of a spherical divergent wave as the object light and a plane wave as the reference light is reproduced by a divergent reproducing light beam from a point farther than the focal point of the hologram. In this second case, the reproducing light beam is converged at such a far point as to enable an magnified scanning operation.
In a third case, a hologram recorded by the mutual interference of a spherical divergent wave as the object light and a spherical convergent wave as the reference light, is reproduced by a divergent reproducing light beam, so that the aberration with respect to a relatively wide range of scanning angle is made small. Such a case is disclosed in Japanese Patent Laying Open No. 54-104849.
In a fourth case, a hologram recorded by the mutual interference of a spherical divergent wave as the object light and a spherical divergent wave as the reference light is reproduced by a convergent reproducing light beam, so that a hologram can be obtained which focusing power is small and which focal length is long.
In the above explained cases, the focusing ability of the hologram is realized by a gradient in the spatial frequency of the interference fringes of the hologram, while the deflecting ability of the hologram is realized by a change in the direction of the interference fringes of the hologram at its reproducing point in accordance with the rotation of the hologram.
The focal length f of the hologram as a focusing lens is approximately given by the following equation (1). EQU 1/f=n.lambda..sub.2 /.lambda..sub.1 (1/Z.sub.0 -1/Z.sub.R) (1)
wherein,
.lambda..sub.1 : wave length of the recording (object and reference) light PA1 .lambda..sub.2 : wave length of the reproducing light beam PA1 n: order of diffraction PA1 Z.sub.0 : distance between the hologram plane and the center of the object light source PA1 Z.sub.R : distance between the hologram plane and the center of the reference light source
The sign of each symbol Z.sub.0 and Z.sub.R is positive in case of the divergent light and negative in case of the convergent light.
The following equation (2) is approximately effected as for the relationship between a distance Z.sub.c and a distance Z.sub.j, which corresponds to the relationship between the object point and the image point, where the Z.sub.c represents the distance from the hologram plane to the reproducing light source, and the Z.sub.j represents the distance from the hologram plane to the image surface. EQU 1/Z.sub.j =1/Z.sub.c +1/f (2)
wherein, the sign of each symbol Z.sub.j and Z.sub.c is positive in the transmitting direction of the reproducing light beam with respect to the hologram plane.
Accordingly, if the hologram having a focal length f is reproduced by a collimated light beam, the diffraction light beam is focused at the focal point of the hologram. If the hologram is reproduced by a divergent or convergent light beam, the diffraction light beam is focused at the image point as assuming the center of the reproducing light source as an object point.
Thus, in the aforementioned first case of the related art in which the diffraction light beam is converged at the focal point, an obtainable scanning length of the diffraction light beam can be as short as about the moving amount of the hologram in company with the rotation of the hologram.
In the aforementioned second case of the related art, the size of the light spot on the image surface can not be made small during the scanning operation since an abrupt change in the image forming length of the hologram happens as the scanning angle increases.
In the aforementioned third case of the related art, since the hologram functions as a focusing lens having a short focal length, a change of the diffraction light beam due to the shift of the optical axis of the hologram is significantly increased. In addition, a large size lens or a concave mirror is necessary in order to converge the reference light onto the hologram recording plane of the hologram disk in the recording process, which is not preferable from a view point of the recording and manufacturing process of the hologram.
In the aformentioned fourth case of the related art, if the hologram is recorded with such a specific condition as Z.sub.0 =Z.sub.R, the hologram having no focusing ability is obtained. Then, if such a spherical light beam as being focused at the image surface is used as the reproducing light beam, the diffraction light beam is also focused at the image surface. Such a hologram is disclosed in Japanese Patent Laying Open No. 60-194419. Thus, it is expected that a small light spot can be obtained at the image surface since the hologram itself hardly has an aberration. However, in this case, since such a reproducing light beam as converging in a great distance is required, the establishment of the reproducing optical system is very difficult.
Accordingly, there is a first problem of those related arts mentioned above that it is difficult to obtain a hologram having both of a sufficient deflecting ability and a sufficient focusing ability.
By the way, in order to enhance the ability of deflecting the reproducing light beam by use of the hologram, recorded in the above mentioned manners, as the hologram in the aforementioned hologram scanner, such a reproducing condition is requested that the diffraction ability of the hologram itself is high and the incident angle of field of the reproducing light beam with respect to the hologram plane is also large, so as to increase the deflection angle of the diffraction light beam.
However, the aberration, of the diffraction light beam as the scanning light beam, at the image surface is inevitably generated to a great extent under such a reproducing condition.
Main aberrations generated in the reproducing operation of the hologram are coma-aberration, astigmatism, and a curvature of field. The coma-aberration is generated in the sub-scanning direction (Yh direction), which is perpendicular to the main scanning direction (Xh direction). The astigmatism and the curvature of field are generated in the main scanning direction. Such aberrations thus generated make it difficult to reduce the size of the light spot formed out of the reproducing light beam on the image surface.
As a countermeasure to the above explained aberrations, the hologram may be recorded to have such interference fringes that the aberration at the image surface in the reproducing operation of the hologram is reduced, by use of the object light and the reference light including aberration to cancel the aberration of the reproducing light beam.
In fact, it is possible to cancel to some extent the aberration of the reproducing light beam by recording the hologram by use of the aberrational wave, which is generated by obliquely inputting a plane wave or a spherical wave to a spherical lens, as the object light or the reference light.
Generally speaking, it is desired in a hologram scanner to make the light spot smaller and thus enable a scanning operation with a higher resolution.
However, in the above mentioned method using the aberrational wave in the recording operation so as to cancel the aberration generated in the reproducing operation, the aberration in the reproducing operation can be only cancelled in either the main scanning direction or the sub-scanning direction. Namely, if the coma-aberration is effectively cancelled, the astigmatism and the curvature of field remain. On the contrary, if the astigmatism and the curvature of field are effectively cancelled, the coma-aberration remains. Consequently, the above mentioned method has a certain fundamental limit to reduce the size of the light spot on the image surface in the reproducing operation of the hologram.